Khaleesi Herbert
2021-02-25
Answered

A university found that of its students withdraw without completing the introductory statistics course. Assume that students registered for the course.
a. Compute the probability that or fewer will withdraw (to 4 decimals).
b. Compute the probability that exactly will withdraw (to 4 decimals).
c. Compute the probability that more than will withdraw (to 4 decimals).

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pivonie8

Answered 2021-02-26
Author has **91** answers

“A university found that of its students withdraw without completing the introductory statistics course” here percentage is not given. Let us assume that p of its student withdraw without completing in the course.The number of students registered for the course is n$X\sim \text{Bin}(n,p)$ Part (a): Compute the probability that or fewer will withdraw (to 4 decimals)Here let us assume that we have to find the probability that m or fever will withdraw.By the definition of mass function of X is given as:$P(X=x)=\left(\begin{array}{}n\\ x\end{array}\right)\times {p}^{x}\times (1-p{)}^{n-x}$

$P(X\le m)=[P(X=0)+P(X=1)+...+P(X=m-1)]$ Part (b): Compute the probability that exactly will withdraw (to 4 decimals).Here also the exact number is not given. Now assume that exactly m’ will withdraw.The probability that exactly m’ will withdraw:$P(X={m}^{\prime})=\left(\begin{array}{c}n\\ {m}^{\prime}\end{array}\right)\times {p}^{x}\times (1-p{)}^{n-m}$ Part (c): Compute the probability that more than M will withdraw (to 4 decimals).Assume that the required number is M.The probability that more than M will withdraw:$P(X>M)=1-P(X\le M)$

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The product of 2 decimals is 20.062 one of the factors has 2 decimals .how many decimals in other factors.

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On average, 3 traffic accidents per month occur at a certain intersection. What is the probability
that in any given month at this intersection

(a) exactly 5 accidents will occur?

(b) fewer than 3 accidents will occur?

(c) at least 2 accidents will occur?

(a) exactly 5 accidents will occur?

(b) fewer than 3 accidents will occur?

(c) at least 2 accidents will occur?

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According to a study by Dr. John McDougall of his live-in weight loss program at St. Helena Hospital, the people who follow his program lose between 6 and 15 pounds a month until they approach trim body weight. Let's suppose that the weight loss is uniformly distributed. We are interested in the weight loss of a randomly selected individual following the program for one month. Give the distribution of X. Enter an exact number as an integer, fraction, or decimal.

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Bethany needs to borrow $\$10,000.$ She can borrow the money at $5.5\mathrm{\%}$ simple interest for 4 yr or she can borrow at $5\mathrm{\%}$ with interest compounded continuously for 4 yr.

a) How much total interest would Bethany pay at$5.5\mathrm{\%}$ simple interest?

b) How much total interest would Bethany pay at$5$ interest compounded continuously?

c) Which option results in less total interest?

a) How much total interest would Bethany pay at

b) How much total interest would Bethany pay at

c) Which option results in less total interest?

asked 2022-06-04

So my task is the following: Consider a sequence of random variables $({X}_{n}{)}_{n\in \mathbb{N}}$ with ${X}_{n}\stackrel{a.s.}{\to}X$ and ${X}_{n}\le B$ a.s. for $B\in \mathbb{R}$. Show that ${X}_{n}\stackrel{{\mathcal{L}}^{p}}{\to}X$ for all $p\in \mathbb{N}$.

My ideas till now:

1. In a first step i tried to show that the expected value is bounded by both sides from zero: $0\le \mathbb{E}(|{X}_{n}-X{|}^{p})\le \dots 0$ Problem here is that i would need that $|{X}_{n}|\le B$ a.s.

2. My second attempt was to use the dominated convergence theorem. With ${Y}_{n}=B$ it follows that if $Y=B$ that ${Y}_{n}\stackrel{a.s.}{\to}Y$ and $\mathbb{E}(|{Y}_{n}-Y|)$. Now I also need that $|{X}_{n}|\le Y$ and then it follows that $\mathbb{E}(|{X}_{n}-X|)\underset{n\to \mathrm{\infty}}{\to}0$.

Probably someone can give me a hint or another way of solving this.

My ideas till now:

1. In a first step i tried to show that the expected value is bounded by both sides from zero: $0\le \mathbb{E}(|{X}_{n}-X{|}^{p})\le \dots 0$ Problem here is that i would need that $|{X}_{n}|\le B$ a.s.

2. My second attempt was to use the dominated convergence theorem. With ${Y}_{n}=B$ it follows that if $Y=B$ that ${Y}_{n}\stackrel{a.s.}{\to}Y$ and $\mathbb{E}(|{Y}_{n}-Y|)$. Now I also need that $|{X}_{n}|\le Y$ and then it follows that $\mathbb{E}(|{X}_{n}-X|)\underset{n\to \mathrm{\infty}}{\to}0$.

Probably someone can give me a hint or another way of solving this.

asked 2021-07-31

Find

asked 2022-08-01

Write the equation of a sine function that has the following characteristics.

Amplitude: 4, Period: $7\pi $ Phase shift: $-\frac{1}{3}$

Type the appropriate values to complete the sine function.

$y=4\mathrm{sin}(?x+?)$

(Use integers or fractions for any numbers in the expression. Simplify your answers.)

Amplitude: 4, Period: $7\pi $ Phase shift: $-\frac{1}{3}$

Type the appropriate values to complete the sine function.

$y=4\mathrm{sin}(?x+?)$

(Use integers or fractions for any numbers in the expression. Simplify your answers.)